"Nor were the 'loremasters' a separate guild of gentle scribes, soon burned by the Orks of Angband upon pyres of books. They were mostly even as Feanor, the greatest, kings, princes and warriors, such as the valiant captains of Gondolin, or Finrod of Nargothrond and Rodothir [> Arothir] his kinsman and steward." - Shibboleth of Feanor
In the Shibboleth Galadriel is described as a loremaster as well.
In the Book of Lost Tales part 2 Idril fights in the Fall of Gondolin. In Shaping of Middle-earth Christopher says Idril was "the prototype of Galadriel".
Galadriel fighting at Alqualondë: "Galadriel’s quarrel with the sons of Fëanor at sack of Alqualondë. How she fought…" - Nature of Middle-earth
Note that the event of fighting at Alqualonde itself is described as a quarrel by Tolkien: "...Thrice the folk of Feanor were driven back, and many were slain upon either side; but the vanguard of the Noldor were succoured by Fingon with the foremost people of Fingolfin. These coming up found a battle joined and their own kin falling, and they rushed in ere they knew rightly the cause of the quarrel: some deemed indeed that the Teleri had sought to waylay the march of the Noldor, at the bidding of the Valar."
There's a marginal note against this passage in Morgoth's Ring: "$149 Marginal note against the passage describing the involvement of the second host in the fighting: 'Finrod and Galadriel (whose husband was of the Teleri) fought against Feanor in defence of Alqualonde.' "
And in Shibboleth: "she fought fiercely against Feanor in defence of her mother's kin."
Note that she wasn't the only female fighter at Alqualondë. Since we are told: "indeed in dire straits or desperate defence the Nissi [the Elf-women] fought valiantly" - Laws and Customs
But the difference between Galadriel and other Nissi was that she wasn't only brave, but she was also a leader and Amazon. "Galadriel, the fairest lady of the house of Finwë and the most valiant." - Morgoth's Ring "[Galadriel] was then of Amazon disposition and bound up her hair as a crown when taking part in athletic feats” - Tolkien Letter 348
“[Éowyn] was also not really a soldier or ‘amazon’, but like many brave women was capable of great military gallantry at a crisis.” - The Letters of JRR Tolkien, Letter #244
The only women in Tolkien who are described as 'amazon' are Haleth (the warrior Queen/Chieftain of Haladin), the early versions of Eowyn in History of Lord of the Rings (she openly goes to war in those versions as opposed to the final version where she wasn't Amazon), Makar's sister the Valie/Goddess of War (from the Book of Lost Tales) and Galadriel. Tolkien translated the word Amazon into "Gothwin" in Elvish, but the literal translation of Gothwin is "War Woman".
"She looked upon the Dwarves also with the eye of a commander, seeing in them the finest warriors to pit against the Orcs" - Unfinished Tales
Galadriel did fight in some wars against Angband like The Battle of the Lammoth and War of Wrath (implied but not explicitly stated). She was there in the Battle of the Lammoth and therefore fought (all elf women fight in such times of crisis), and according to History of Middle-earth Eonwë summoned all free people and birds and beasts to fight in War of Wrath, only cowards rejected his summons ("but the power and dread of Morgoth was great and many did not obey his summons"). Galadriel wasn't such. The reason Galadriel and Celeborn hadn't fought in previous battles against Angband is not because they weren't good warriors, the reason was... "they did not join in the war against Angband, which they judged to be hopeless under the ban of the Valar and without their aid; and their counsel was... " - Unfinished Tales
Nobody listened to their counsel about forming that alliance, and the Valar didn't send aid until War of Wrath, henceforth Celeborn and Galadriel thought it's useless if they waste their energy in that war as long as there's no hope. But when hope came, there was no reason for them to not join in the war. Even random Elves of Eriador answered the summons to fight when they heard of new come hope.
In the versions of Galadriel where her boyfriend/husband was from Doriath she also gone through some of the events of the Ruin of Beleriand (here it is never said if she had left Doriath before its fall and indeed it is stated she only crossed the mountains into Eriador in the Second Age and indeed it is even stated in a note about Celeborn that he was present in the sack of Doriath), all meaning/implying she was there in the Ruin of Doriath and the Third Kinslaying and such (as is also pointed out by Christopher Tolkien himself). We know female Elves fought in such times of crisis, even if they weren't Amazon.
In Second Age Galadriel was one of the war leaders of Eregion in the War of the Elves and Sauron. In the early versions Galadriel is not present in Eregion during the war (she was in Lorien), and it's her husband and Celebrimbor (and later Elrond) only who lead the armies of Eregion: "The scouts and vanguard of Sauron's host were already approaching when Celeborn made a sortie and drove them back; but though he was able to join his force to that of Elrond...." - Unfinished Tales
But in later essays and notes Galadriel is there right side-by-side with Celeborn: “Galadriel and Celeborn, and their followers, who after the destruction of Eregion passed through Moria” “Galadriel and Celeborn only retreated thither [to Lorien] after the downfall of Eregion." “After the Fall of Eregion... They had passed through Moria with considerable following of Noldorin Exiles and dwelt for many years in Lorien” In Eregion Galadriel and Celeborn took part "in its defence against Sauron"
Above quotes are from Parma Eldalamberon 17 and Nature of Middle-earth.
In Unfinished Tales there's yet another wholly different version of Galadriel during the WotE&S where she apparently retreated from Eregion after its fall and "joined with Gil-Galad in Lindon". I should note that the Battle of Eregion was long, Sauron assaulted Eriador in 1695 and Eregion fell in 1697. Then three years later or so Sauron assaulted Lindon. So going by this other version of Galadriel where she retreated to Lindon, she most likely also fought in the rest of the War of the Elves and Sauron.
The argument that all Elf healers aren't warriors does not hold up. It's explicitly stated that this was some Elf belief, meaning not necessarily a truth/fact. Elrond fought in War of Wrath, War of the Elves and Sauron, and War of the Last Alliance, until he retired from warrior state in Third Age and yet he was the greatest healer. Beleg killed the enemies all the time 24/7 and yet he remained a great healer.
In Peoples of Middle-earth and Unfinished Tales and Morgoth's Ring everytime Tolkien describes young Galadriel he feels the need to write "she was (both physically and mentally) strong, brave" "she was valiant" etc. Also same thing can be seen often in Nature of Middle-earth. "She was called Nerwen ‘man-maiden’ because of her strength and stature, and her courage."
The assumption that Galadriel wasn't in the Last Alliance is just an assumption with no proof. We don't know where she was during the Last Alliance, Tolkien never specified where was Galadriel in late SA. Though it's too many times stated and pointed out she was willing to do her best against Sauron and Sauron himself thought of her as his chief enemy.
Also her desiring to avenge her brother is canon. It's stated Finrod was "of all her kin the nearest to her heart" and she "esteemed him and loved him". Finrod gave his life to save Beren against the werewolf that Sauron had sent to eat Beren in dungeons of Sauron. "She was sister of Finrod Felagund, Friend-of-Men, once king of Nargothrond, who gave his life to save Beren son of Barahir." - Appendix
'Aegnor is gone, Angrod is gone, and Felagund is no more. Of Finarfin's children I am the last. But my heart is still proud. What wrong did the Golden House of Finarfin do that I should ask the pardon of the Valar...' - Galadriel
"Pride still moved her when, at the end of the Elder Days after the final overthrow of Morgoth, she refused the pardon of the Valar for all who had fought against him, "
"she deemed it her duty to remain in Middle-earth while Sauron was still unconquered" - UT